1105 (number)

1105 1, 5, 13, 17, 65, 85, 221, 1105 1105 (eleven hundred [and] five, or one thousand one hundred [and] five) is the natural number following 1104 and preceding 1106. Mathematical properties 1105 is the smallest positive integer that is a sum of two positive squares in exactly four different ways,A016032 Least positive integer that is the sum of two squares of positive integers in exactly n ways a property that can be connected (via the sum of two squares theorem) to its factorization 5 × 13 × 17 as the product of the three smallest prime numbers that are congruent to 1 modulo 4. Tenenbaum Gérald Gérald Tenenbaum Graham Ronald L. Ronald Graham Nešetřil Jaroslav Jaroslav Nešetřil 1105: first steps in a mysterious quest 10.1007/978-3-642-60408-9_21 1425191 268–275 Springer Berlin Algorithms and Combinatorics The mathematics of Paul Erdős, I 13 1997 978-3-642-64394-1 A006278 product of the first n primes congruent to 1 (mod 4) It is also the second-smallest Carmichael number, after 561,A002997 Carmichael numbers Křížek Michal Luca Florian Somer Lawrence 10.1007/978-0-387-21850-2 0-387-95332-9 1866957 136 Springer-Verlag, New York CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 17 Lectures on Fermat Numbers: From Number Theory to Geometry https://books.google.com/books?id=hgfSBwAAQBAJ&pg=PA136 9 2001 one of the first four Carmichael numbers identified by R. D. Carmichael in his 1910 paper introducing this concept. Carmichael R. D. Robert Daniel Carmichael 10.1090/S0002-9904-1910-01892-9 Bulletin of the American Mathematical Society 232–238 Note on a new number theory function https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-16/issue-5/Note-on-a-new-number-theory-function/bams/1183420617.full 16 1910 5 41.0226.04 free It is also a Fermat pseudoprime,A001567 Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers a decagonal number, and a centered square number.Vanovschi Vitalii Properties of the number 1105 http://www.numberempire.com:80/1105 2026-09-17 www.numberempire.com en It is a member of the Moser–de Bruijn sequence of sums of distinct powers of four.A000695 Moser-de Bruijn sequence References 10 Category:Integers